MinT - Information on Result #869313

Information on Result #869313

Linear OOA(32⁴⁰, 16385, F₃₂, 2, 14) (dual of [(16385, 2), 32730, 15]-NRT-code), using OOA 2-folding based on linear OA(32⁴⁰, 32770, F₃₂, 14) (dual of [32770, 32730, 15]-code), using

discarding factors / shortening the dual code based on linear OA(32⁴⁰, 32771, F₃₂, 14) (dual of [32771, 32731, 15]-code), using
- constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
  1. linear OA(32⁴⁰, 32768, F₃₂, 14) (dual of [32768, 32728, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  2. linear OA(32³⁷, 32768, F₃₂, 13) (dual of [32768, 32731, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(32⁰, 3, F₃₂, 0) (dual of [3, 3, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(32⁴⁷, 16418, F₃₂, 2, 14) (dual of [(16418, 2), 32789, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁴⁸, 16429, F₃₂, 2, 14) (dual of [(16429, 2), 32810, 15]-NRT-code)	[i]
3	Linear OOA(32⁵⁰, 16451, F₃₂, 2, 14) (dual of [(16451, 2), 32852, 15]-NRT-code)	[i]
4	Linear OOA(32⁵¹, 16462, F₃₂, 2, 14) (dual of [(16462, 2), 32873, 15]-NRT-code)	[i]
5	Linear OOA(32⁵², 16473, F₃₂, 2, 14) (dual of [(16473, 2), 32894, 15]-NRT-code)	[i]
6	Linear OOA(32⁵², 16484, F₃₂, 2, 14) (dual of [(16484, 2), 32916, 15]-NRT-code)	[i]
7	Digital (26, 40, 16385)-net over F₃₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound